utils.py

# -*- coding: utf-8 -*-
"""Utility functions for plotting M/EEG data."""

# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
#          Denis Engemann <denis.engemann@gmail.com>
#          Martin Luessi <mluessi@nmr.mgh.harvard.edu>
#          Eric Larson <larson.eric.d@gmail.com>
#          Mainak Jas <mainak@neuro.hut.fi>
#          Stefan Appelhoff <stefan.appelhoff@mailbox.org>
#          Clemens Brunner <clemens.brunner@gmail.com>
#          Daniel McCloy <dan@mccloy.info>
#
# License: Simplified BSD

from collections import defaultdict
from contextlib import contextmanager
from functools import partial
import difflib
import webbrowser
import tempfile
import math
import numpy as np
from copy import deepcopy
from distutils.version import LooseVersion
import warnings

from ..defaults import _handle_default
from ..fixes import _get_status
from ..io import show_fiff, Info
from ..io.constants import FIFF
from ..io.pick import (channel_type, channel_indices_by_type, pick_channels,
                       _pick_data_channels, _DATA_CH_TYPES_SPLIT,
                       _DATA_CH_TYPES_ORDER_DEFAULT, _VALID_CHANNEL_TYPES,
                       pick_info, _picks_by_type, pick_channels_cov,
                       _contains_ch_type)
from ..io.meas_info import create_info
from ..rank import compute_rank
from ..io.proj import setup_proj
from ..utils import (verbose, get_config, warn, _check_ch_locs, _check_option,
                     logger, fill_doc, _pl, _check_sphere, _ensure_int)

from ..selection import (read_selection, _SELECTIONS, _EEG_SELECTIONS,
                         _divide_to_regions)
from ..transforms import apply_trans


_channel_type_prettyprint = {'eeg': "EEG channel", 'grad': "Gradiometer",
                             'mag': "Magnetometer", 'seeg': "sEEG channel",
                             'eog': "EOG channel", 'ecg': "ECG sensor",
                             'emg': "EMG sensor", 'ecog': "ECoG channel",
                             'misc': "miscellaneous sensor"}


def _setup_vmin_vmax(data, vmin, vmax, norm=False):
    """Handle vmin and vmax parameters for visualizing topomaps.

    For the normal use-case (when `vmin` and `vmax` are None), the parameter
    `norm` drives the computation. When norm=False, data is supposed to come
    from a mag and the output tuple (vmin, vmax) is symmetric range
    (-x, x) where x is the max(abs(data)). When norm=True (a.k.a. data is the
    L2 norm of a gradiometer pair) the output tuple corresponds to (0, x).

    Otherwise, vmin and vmax are callables that drive the operation.
    """
    should_warn = False
    if vmax is None and vmin is None:
        vmax = np.abs(data).max()
        vmin = 0. if norm else -vmax
        if vmin == 0 and np.min(data) < 0:
            should_warn = True

    else:
        if callable(vmin):
            vmin = vmin(data)
        elif vmin is None:
            vmin = 0. if norm else np.min(data)
            if vmin == 0 and np.min(data) < 0:
                should_warn = True

        if callable(vmax):
            vmax = vmax(data)
        elif vmax is None:
            vmax = np.max(data)

    if should_warn:
        warn_msg = ("_setup_vmin_vmax output a (min={vmin}, max={vmax})"
                    " range whereas the minimum of data is {data_min}")
        warn_val = {'vmin': vmin, 'vmax': vmax, 'data_min': np.min(data)}
        warn(warn_msg.format(**warn_val), UserWarning)

    return vmin, vmax


def plt_show(show=True, fig=None, **kwargs):
    """Show a figure while suppressing warnings.

    Parameters
    ----------
    show : bool
        Show the figure.
    fig : instance of Figure | None
        If non-None, use fig.show().
    **kwargs : dict
        Extra arguments for :func:`matplotlib.pyplot.show`.
    """
    from matplotlib import get_backend
    import matplotlib.pyplot as plt
    if show and get_backend() != 'agg':
        (fig or plt).show(**kwargs)


def tight_layout(pad=1.2, h_pad=None, w_pad=None, fig=None):
    """Adjust subplot parameters to give specified padding.

    .. note:: For plotting please use this function instead of
              ``plt.tight_layout``.

    Parameters
    ----------
    pad : float
        Padding between the figure edge and the edges of subplots, as a
        fraction of the font-size.
    h_pad : float
        Padding height between edges of adjacent subplots.
        Defaults to ``pad_inches``.
    w_pad : float
        Padding width between edges of adjacent subplots.
        Defaults to ``pad_inches``.
    fig : instance of Figure
        Figure to apply changes to.

    Notes
    -----
    This will not force constrained_layout=False if the figure was created
    with that method.
    """
    import matplotlib.pyplot as plt
    fig = plt.gcf() if fig is None else fig

    fig.canvas.draw()
    constrained = fig.get_constrained_layout()
    if constrained:
        return  # no-op
    try:  # see https://github.com/matplotlib/matplotlib/issues/2654
        with warnings.catch_warnings(record=True) as ws:
            fig.tight_layout(pad=pad, h_pad=h_pad, w_pad=w_pad)
    except Exception:
        try:
            with warnings.catch_warnings(record=True) as ws:
                fig.set_tight_layout(dict(pad=pad, h_pad=h_pad, w_pad=w_pad))
        except Exception:
            warn('Matplotlib function "tight_layout" is not supported.'
                 ' Skipping subplot adjustment.')
            return
    for w in ws:
        w_msg = str(w.message) if hasattr(w, 'message') else w.get_message()
        if not w_msg.startswith('This figure includes Axes'):
            warn(w_msg, w.category, 'matplotlib')


def _check_delayed_ssp(container):
    """Handle interactive SSP selection."""
    if container.proj is True or\
       all(p['active'] for p in container.info['projs']):
        raise RuntimeError('Projs are already applied. Please initialize'
                           ' the data with proj set to False.')
    elif len(container.info['projs']) < 1:
        raise RuntimeError('No projs found in evoked.')


def _validate_if_list_of_axes(axes, obligatory_len=None):
    """Validate whether input is a list/array of axes."""
    from matplotlib.axes import Axes
    if obligatory_len is not None and not isinstance(obligatory_len, int):
        raise ValueError('obligatory_len must be None or int, got %d',
                         'instead' % type(obligatory_len))
    if not isinstance(axes, (list, np.ndarray)):
        raise ValueError('axes must be a list or numpy array of matplotlib '
                         'axes objects, got %s instead.' % type(axes))
    if isinstance(axes, np.ndarray) and axes.ndim > 1:
        raise ValueError('if input is a numpy array, it must be '
                         'one-dimensional. The received numpy array has %d '
                         'dimensions however. Try using ravel or flatten '
                         'method of the array.' % axes.ndim)
    is_correct_type = np.array([isinstance(x, Axes)
                                for x in axes])
    if not np.all(is_correct_type):
        first_bad = np.where(np.logical_not(is_correct_type))[0][0]
        raise ValueError('axes must be a list or numpy array of matplotlib '
                         'axes objects while one of the list elements is '
                         '%s.' % type(axes[first_bad]))
    if obligatory_len is not None and not len(axes) == obligatory_len:
        raise ValueError('axes must be a list/array of length %d, while the'
                         ' length is %d' % (obligatory_len, len(axes)))


def mne_analyze_colormap(limits=[5, 10, 15], format='mayavi'):
    """Return a colormap similar to that used by mne_analyze.

    Parameters
    ----------
    limits : list (or array) of length 3 or 6
        Bounds for the colormap, which will be mirrored across zero if length
        3, or completely specified (and potentially asymmetric) if length 6.
    format : str
        Type of colormap to return. If 'matplotlib', will return a
        matplotlib.colors.LinearSegmentedColormap. If 'mayavi', will
        return an RGBA array of shape (256, 4).

    Returns
    -------
    cmap : instance of colormap | array
        A teal->blue->gray->red->yellow colormap. See docstring of the 'format'
        argument for further details.

    Notes
    -----
    For this will return a colormap that will display correctly for data
    that are scaled by the plotting function to span [-fmax, fmax].
    """  # noqa: E501
    # Ensure limits is an array
    limits = np.asarray(limits, dtype='float')

    if len(limits) != 3 and len(limits) != 6:
        raise ValueError('limits must have 3 or 6 elements')
    if len(limits) == 3 and any(limits < 0.):
        raise ValueError('if 3 elements, limits must all be non-negative')
    if any(np.diff(limits) <= 0):
        raise ValueError('limits must be monotonically increasing')
    if format == 'matplotlib':
        from matplotlib import colors
        if len(limits) == 3:
            limits = (np.concatenate((-np.flipud(limits), limits)) +
                      limits[-1]) / (2 * limits[-1])
        else:
            limits = (limits - np.min(limits)) / np.max(limits -
                                                        np.min(limits))

        cdict = {'red': ((limits[0], 0.0, 0.0),
                         (limits[1], 0.0, 0.0),
                         (limits[2], 0.5, 0.5),
                         (limits[3], 0.5, 0.5),
                         (limits[4], 1.0, 1.0),
                         (limits[5], 1.0, 1.0)),
                 'green': ((limits[0], 1.0, 1.0),
                           (limits[1], 0.0, 0.0),
                           (limits[2], 0.5, 0.5),
                           (limits[3], 0.5, 0.5),
                           (limits[4], 0.0, 0.0),
                           (limits[5], 1.0, 1.0)),
                 'blue': ((limits[0], 1.0, 1.0),
                          (limits[1], 1.0, 1.0),
                          (limits[2], 0.5, 0.5),
                          (limits[3], 0.5, 0.5),
                          (limits[4], 0.0, 0.0),
                          (limits[5], 0.0, 0.0)),
                 'alpha': ((limits[0], 1.0, 1.0),
                           (limits[1], 1.0, 1.0),
                           (limits[2], 0.0, 0.0),
                           (limits[3], 0.0, 0.0),
                           (limits[4], 1.0, 1.0),
                           (limits[5], 1.0, 1.0)),
                 }
        return colors.LinearSegmentedColormap('mne_analyze', cdict)
    elif format == 'mayavi':
        if len(limits) == 3:
            limits = np.concatenate((-np.flipud(limits), [0], limits)) /\
                limits[-1]
        else:
            limits = np.concatenate((limits[:3], [0], limits[3:]))
            limits /= np.max(np.abs(limits))
        r = np.array([0, 0, 0, 0, 1, 1, 1])
        g = np.array([1, 0, 0, 0, 0, 0, 1])
        b = np.array([1, 1, 1, 0, 0, 0, 0])
        a = np.array([1, 1, 0, 0, 0, 1, 1])
        xp = (np.arange(256) - 128) / 128.0
        colormap = np.r_[[np.interp(xp, limits, 255 * c)
                          for c in [r, g, b, a]]].T
        return colormap
    else:
        raise ValueError('format must be either matplotlib or mayavi')


@contextmanager
def _events_off(obj):
    obj.eventson = False
    try:
        yield
    finally:
        obj.eventson = True


def _toggle_proj(event, params, all_=False):
    """Perform operations when proj boxes clicked."""
    # read options if possible
    if 'proj_checks' in params:
        bools = _get_status(params['proj_checks'])
        if all_:
            new_bools = [not all(bools)] * len(bools)
            with _events_off(params['proj_checks']):
                for bi, (old, new) in enumerate(zip(bools, new_bools)):
                    if old != new:
                        params['proj_checks'].set_active(bi)
                        bools[bi] = new
        for bi, (b, p) in enumerate(zip(bools, params['projs'])):
            # see if they tried to deactivate an active one
            if not b and p['active']:
                bools[bi] = True
    else:
        proj = params.get('apply_proj', True)
        bools = [proj] * len(params['projs'])

    compute_proj = False
    if 'proj_bools' not in params:
        compute_proj = True
    elif not np.array_equal(bools, params['proj_bools']):
        compute_proj = True

    # if projectors changed, update plots
    if compute_proj is True:
        params['plot_update_proj_callback'](params, bools)


def _get_channel_plotting_order(order, ch_types, picks=None):
    """Determine channel plotting order for browse-style Raw/Epochs plots."""
    if order is None:
        # for backward compat, we swap the first two to keep grad before mag
        ch_type_order = list(_DATA_CH_TYPES_ORDER_DEFAULT)
        ch_type_order = tuple(['grad', 'mag'] + ch_type_order[2:])
        order = [pick_idx for order_type in ch_type_order
                 for pick_idx, pick_type in enumerate(ch_types)
                 if order_type == pick_type]
    elif not isinstance(order, (np.ndarray, list, tuple)):
        raise ValueError('order should be array-like; got '
                         f'"{order}" ({type(order)}).')
    if picks is not None:
        order = [ch for ch in order if ch in picks]
    return np.asarray(order)


def _make_event_color_dict(event_color, events=None, event_id=None):
    """Make or validate a dict mapping event ids to colors."""
    from .misc import _handle_event_colors
    if isinstance(event_color, dict):  # if event_color is a dict, validate it
        event_id = dict() if event_id is None else event_id
        event_color = {_ensure_int(event_id.get(key, key), 'event_color key'):
                       value for key, value in event_color.items()}
        default = event_color.pop(-1, None)
        default_factory = None if default is None else lambda: default
        new_dict = defaultdict(default_factory)
        for key, value in event_color.items():
            if key < 1:
                raise KeyError('event_color keys must be strictly positive, '
                               f'or -1 (cannot use {key})')
            new_dict[key] = value
        return new_dict
    elif event_color is None:  # make a dict from color cycle
        uniq_events = set() if events is None else np.unique(events[:, 2])
        return _handle_event_colors(event_color, uniq_events, event_id)
    else:  # if event_color is a MPL color-like thing, use it for all events
        return defaultdict(lambda: event_color)


def _prepare_trellis(n_cells, ncols, nrows='auto', title=False, colorbar=False,
                     size=1.3):
    import matplotlib.pyplot as plt
    from matplotlib.gridspec import GridSpec

    if n_cells == 1:
        nrows = ncols = 1
    elif isinstance(ncols, int) and n_cells <= ncols:
        nrows, ncols = 1, n_cells
    else:
        if ncols == 'auto' and nrows == 'auto':
            nrows = math.floor(math.sqrt(n_cells))
            ncols = math.ceil(n_cells / nrows)
        elif ncols == 'auto':
            ncols = math.ceil(n_cells / nrows)
        elif nrows == 'auto':
            nrows = math.ceil(n_cells / ncols)
        else:
            naxes = ncols * nrows
            if naxes < n_cells:
                raise ValueError("Cannot plot {} axes in a {} by {} "
                                 "figure.".format(n_cells, nrows, ncols))

    if colorbar:
        ncols += 1
    width = size * ncols
    height = (size + max(0, 0.1 * (4 - size))) * nrows + bool(title) * 0.5
    height_ratios = None
    g_kwargs = {}
    figure_nobar(figsize=(width * 1.5, height * 1.5))
    gs = GridSpec(nrows, ncols, height_ratios=height_ratios, **g_kwargs)

    axes = []
    if colorbar:
        # exclude last axis of each row except top row, which is for colorbar
        exclude = set(range(2 * ncols - 1, nrows * ncols, ncols))
        ax_idxs = sorted(set(range(nrows * ncols)) - exclude)[:n_cells + 1]
    else:
        ax_idxs = range(n_cells)
    for ax_idx in ax_idxs:
        axes.append(plt.subplot(gs[ax_idx]))

    fig = axes[0].get_figure()

    return fig, axes, ncols, nrows


def _draw_proj_checkbox(event, params, draw_current_state=True):
    """Toggle options (projectors) dialog."""
    from matplotlib import widgets
    projs = params['projs']
    # turn on options dialog

    labels = [p['desc'] for p in projs]
    actives = ([p['active'] for p in projs] if draw_current_state else
               params.get('proj_bools', [params['apply_proj']] * len(projs)))

    width = max([4., max([len(p['desc']) for p in projs]) / 6.0 + 0.5])
    height = (len(projs) + 1) / 6.0 + 1.5
    fig_proj = figure_nobar(figsize=(width, height))
    _set_window_title(fig_proj, 'SSP projection vectors')
    offset = (1. / 6. / height)
    params['fig_proj'] = fig_proj  # necessary for proper toggling
    ax_temp = fig_proj.add_axes((0, offset, 1, 0.8 - offset), frameon=False)
    ax_temp.set_title('Projectors marked with "X" are active')

    proj_checks = widgets.CheckButtons(ax_temp, labels=labels, actives=actives)
    # make edges around checkbox areas
    for rect in proj_checks.rectangles:
        rect.set_edgecolor('0.5')
        rect.set_linewidth(1.)

    # change already-applied projectors to red
    for ii, p in enumerate(projs):
        if p['active']:
            for x in proj_checks.lines[ii]:
                x.set_color('#ff0000')
    # make minimal size
    # pass key presses from option dialog over

    proj_checks.on_clicked(partial(_toggle_proj, params=params))
    params['proj_checks'] = proj_checks
    fig_proj.canvas.mpl_connect('key_press_event', _key_press)

    # Toggle all
    ax_temp = fig_proj.add_axes((0, 0, 1, offset), frameon=False)
    proj_all = widgets.Button(ax_temp, 'Toggle all')
    proj_all.on_clicked(partial(_toggle_proj, params=params, all_=True))
    params['proj_all'] = proj_all

    # this should work for non-test cases
    try:
        fig_proj.canvas.draw()
        plt_show(fig=fig_proj, warn=False)
    except Exception:
        pass


def _simplify_float(label):
    # Heuristic to turn floats to ints where possible (e.g. -500.0 to -500)
    if isinstance(label, float) and np.isfinite(label) and \
            float(str(label)) != round(label):
        label = round(label, 2)
    return label


def _get_figsize_from_config():
    """Get default / most recent figure size from config."""
    figsize = get_config('MNE_BROWSE_RAW_SIZE')
    if figsize is not None:
        figsize = figsize.split(',')
        figsize = tuple([float(s) for s in figsize])
    return figsize


@verbose
def compare_fiff(fname_1, fname_2, fname_out=None, show=True, indent='    ',
                 read_limit=np.inf, max_str=30, verbose=None):
    """Compare the contents of two fiff files using diff and show_fiff.

    Parameters
    ----------
    fname_1 : str
        First file to compare.
    fname_2 : str
        Second file to compare.
    fname_out : str | None
        Filename to store the resulting diff. If None, a temporary
        file will be created.
    show : bool
        If True, show the resulting diff in a new tab in a web browser.
    indent : str
        How to indent the lines.
    read_limit : int
        Max number of bytes of data to read from a tag. Can be np.inf
        to always read all data (helps test read completion).
    max_str : int
        Max number of characters of string representation to print for
        each tag's data.
    %(verbose)s

    Returns
    -------
    fname_out : str
        The filename used for storing the diff. Could be useful for
        when a temporary file is used.
    """
    file_1 = show_fiff(fname_1, output=list, indent=indent,
                       read_limit=read_limit, max_str=max_str)
    file_2 = show_fiff(fname_2, output=list, indent=indent,
                       read_limit=read_limit, max_str=max_str)
    diff = difflib.HtmlDiff().make_file(file_1, file_2, fname_1, fname_2)
    if fname_out is not None:
        f = open(fname_out, 'wb')
    else:
        f = tempfile.NamedTemporaryFile('wb', delete=False, suffix='.html')
        fname_out = f.name
    with f as fid:
        fid.write(diff.encode('utf-8'))
    if show is True:
        webbrowser.open_new_tab(fname_out)
    return fname_out


def figure_nobar(*args, **kwargs):
    """Make matplotlib figure with no toolbar.

    Parameters
    ----------
    *args : list
        Arguments to pass to :func:`matplotlib.pyplot.figure`.
    **kwargs : dict
        Keyword arguments to pass to :func:`matplotlib.pyplot.figure`.

    Returns
    -------
    fig : instance of Figure
        The figure.
    """
    from matplotlib import rcParams, pyplot as plt
    old_val = rcParams['toolbar']
    try:
        rcParams['toolbar'] = 'none'
        fig = plt.figure(*args, **kwargs)
        # remove button press catchers (for toolbar)
        cbs = list(fig.canvas.callbacks.callbacks['key_press_event'].keys())
        for key in cbs:
            fig.canvas.callbacks.disconnect(key)
    finally:
        rcParams['toolbar'] = old_val
    return fig


def _show_help(col1, col2, width, height):
    fig_help = figure_nobar(figsize=(width, height), dpi=80)
    _set_window_title(fig_help, 'Help')

    ax = fig_help.add_subplot(111)
    celltext = [[c1, c2] for c1, c2 in zip(col1.strip().split("\n"),
                                           col2.strip().split("\n"))]
    table = ax.table(cellText=celltext, loc="center", cellLoc="left")
    table.auto_set_font_size(False)
    table.set_fontsize(12)
    ax.set_axis_off()
    for (row, col), cell in table.get_celld().items():
        cell.set_edgecolor(None)  # remove cell borders
        # right justify, following:
        # https://stackoverflow.com/questions/48210749/matplotlib-table-assign-different-text-alignments-to-different-columns?rq=1  # noqa: E501
        if col == 0:
            cell._loc = 'right'

    fig_help.canvas.mpl_connect('key_press_event', _key_press)

    # this should work for non-test cases
    try:
        fig_help.canvas.draw()
        plt_show(fig=fig_help, warn=False)
    except Exception:
        pass


def _key_press(event):
    """Handle key press in dialog."""
    import matplotlib.pyplot as plt
    if event.key == 'escape':
        plt.close(event.canvas.figure)


class ClickableImage(object):
    """Display an image so you can click on it and store x/y positions.

    Takes as input an image array (can be any array that works with imshow,
    but will work best with images.  Displays the image and lets you
    click on it.  Stores the xy coordinates of each click, so now you can
    superimpose something on top of it.

    Upon clicking, the x/y coordinate of the cursor will be stored in
    self.coords, which is a list of (x, y) tuples.

    Parameters
    ----------
    imdata : ndarray
        The image that you wish to click on for 2-d points.
    **kwargs : dict
        Keyword arguments. Passed to ax.imshow.

    Notes
    -----
    .. versionadded:: 0.9.0
    """

    def __init__(self, imdata, **kwargs):
        """Display the image for clicking."""
        import matplotlib.pyplot as plt
        self.coords = []
        self.imdata = imdata
        self.fig = plt.figure()
        self.ax = self.fig.add_subplot(111)
        self.ymax = self.imdata.shape[0]
        self.xmax = self.imdata.shape[1]
        self.im = self.ax.imshow(imdata,
                                 extent=(0, self.xmax, 0, self.ymax),
                                 picker=True, **kwargs)
        self.ax.axis('off')
        self.fig.canvas.mpl_connect('pick_event', self.onclick)
        plt_show(block=True)

    def onclick(self, event):
        """Handle Mouse clicks.

        Parameters
        ----------
        event : matplotlib.backend_bases.Event
            The matplotlib object that we use to get x/y position.
        """
        mouseevent = event.mouseevent
        self.coords.append((mouseevent.xdata, mouseevent.ydata))

    def plot_clicks(self, **kwargs):
        """Plot the x/y positions stored in self.coords.

        Parameters
        ----------
        **kwargs : dict
            Arguments are passed to imshow in displaying the bg image.
        """
        import matplotlib.pyplot as plt
        if len(self.coords) == 0:
            raise ValueError('No coordinates found, make sure you click '
                             'on the image that is first shown.')
        f, ax = plt.subplots()
        ax.imshow(self.imdata, extent=(0, self.xmax, 0, self.ymax), **kwargs)
        xlim, ylim = [ax.get_xlim(), ax.get_ylim()]
        xcoords, ycoords = zip(*self.coords)
        ax.scatter(xcoords, ycoords, c='#ff0000')
        ann_text = np.arange(len(self.coords)).astype(str)
        for txt, coord in zip(ann_text, self.coords):
            ax.annotate(txt, coord, fontsize=20, color='#ff0000')
        ax.set_xlim(xlim)
        ax.set_ylim(ylim)
        plt_show()

    def to_layout(self, **kwargs):
        """Turn coordinates into an MNE Layout object.

        Normalizes by the image you used to generate clicks

        Parameters
        ----------
        **kwargs : dict
            Arguments are passed to generate_2d_layout.

        Returns
        -------
        layout : instance of Layout
            The layout.
        """
        from ..channels.layout import generate_2d_layout
        coords = np.array(self.coords)
        lt = generate_2d_layout(coords, bg_image=self.imdata, **kwargs)
        return lt


def _fake_click(fig, ax, point, xform='ax', button=1, kind='press'):
    """Fake a click at a relative point within axes."""
    if xform == 'ax':
        x, y = ax.transAxes.transform_point(point)
    elif xform == 'data':
        x, y = ax.transData.transform_point(point)
    else:
        assert xform == 'pix'
        x, y = point
    if kind == 'press':
        func = partial(fig.canvas.button_press_event, x=x, y=y, button=button)
    elif kind == 'release':
        func = partial(fig.canvas.button_release_event, x=x, y=y,
                       button=button)
    elif kind == 'motion':
        func = partial(fig.canvas.motion_notify_event, x=x, y=y)
    func(guiEvent=None)


def add_background_image(fig, im, set_ratios=None):
    """Add a background image to a plot.

    Adds the image specified in ``im`` to the
    figure ``fig``. This is generally meant to
    be done with topo plots, though it could work
    for any plot.

    .. note:: This modifies the figure and/or axes in place.

    Parameters
    ----------
    fig : Figure
        The figure you wish to add a bg image to.
    im : array, shape (M, N, {3, 4})
        A background image for the figure. This must be a valid input to
        `matplotlib.pyplot.imshow`. Defaults to None.
    set_ratios : None | str
        Set the aspect ratio of any axes in fig
        to the value in set_ratios. Defaults to None,
        which does nothing to axes.

    Returns
    -------
    ax_im : instance of Axes
        Axes created corresponding to the image you added.

    Notes
    -----
    .. versionadded:: 0.9.0
    """
    if im is None:
        # Don't do anything and return nothing
        return None
    if set_ratios is not None:
        for ax in fig.axes:
            ax.set_aspect(set_ratios)

    ax_im = fig.add_axes([0, 0, 1, 1], label='background')
    ax_im.imshow(im, aspect='auto')
    ax_im.set_zorder(-1)
    return ax_im


def _find_peaks(evoked, npeaks):
    """Find peaks from evoked data.

    Returns ``npeaks`` biggest peaks as a list of time points.
    """
    from scipy.signal import argrelmax
    gfp = evoked.data.std(axis=0)
    order = len(evoked.times) // 30
    if order < 1:
        order = 1
    peaks = argrelmax(gfp, order=order, axis=0)[0]
    if len(peaks) > npeaks:
        max_indices = np.argsort(gfp[peaks])[-npeaks:]
        peaks = np.sort(peaks[max_indices])
    times = evoked.times[peaks]
    if len(times) == 0:
        times = [evoked.times[gfp.argmax()]]
    return times


def _process_times(inst, use_times, n_peaks=None, few=False):
    """Return a list of times for topomaps."""
    if isinstance(use_times, str):
        if use_times == 'interactive':
            use_times, n_peaks = 'peaks', 1
        if use_times == 'peaks':
            if n_peaks is None:
                n_peaks = min(3 if few else 7, len(inst.times))
            use_times = _find_peaks(inst, n_peaks)
        elif use_times == 'auto':
            if n_peaks is None:
                n_peaks = min(5 if few else 10, len(use_times))
            use_times = np.linspace(inst.times[0], inst.times[-1], n_peaks)
        else:
            raise ValueError("Got an unrecognized method for `times`. Only "
                             "'peaks', 'auto' and 'interactive' are supported "
                             "(or directly passing numbers).")
    elif np.isscalar(use_times):
        use_times = [use_times]

    use_times = np.array(use_times, float)

    if use_times.ndim != 1:
        raise ValueError('times must be 1D, got %d dimensions'
                         % use_times.ndim)

    if len(use_times) > 25:
        warn('More than 25 topomaps plots requested. This might take a while.')

    return use_times


@verbose
def plot_sensors(info, kind='topomap', ch_type=None, title=None,
                 show_names=False, ch_groups=None, to_sphere=True, axes=None,
                 block=False, show=True, sphere=None, verbose=None):
    """Plot sensors positions.

    Parameters
    ----------
    info : instance of Info
        Info structure containing the channel locations.
    kind : str
        Whether to plot the sensors as 3d, topomap or as an interactive
        sensor selection dialog. Available options 'topomap', '3d', 'select'.
        If 'select', a set of channels can be selected interactively by using
        lasso selector or clicking while holding control key. The selected
        channels are returned along with the figure instance. Defaults to
        'topomap'.
    ch_type : None | str
        The channel type to plot. Available options 'mag', 'grad', 'eeg',
        'seeg', 'ecog', 'all'. If ``'all'``, all the available mag, grad, eeg,
        seeg and ecog channels are plotted. If None (default), then channels
        are chosen in the order given above.
    title : str | None
        Title for the figure. If None (default), equals to
        ``'Sensor positions (%%s)' %% ch_type``.
    show_names : bool | array of str
        Whether to display all channel names. If an array, only the channel
        names in the array are shown. Defaults to False.
    ch_groups : 'position' | array of shape (n_ch_groups, n_picks) | None
        Channel groups for coloring the sensors. If None (default), default
        coloring scheme is used. If 'position', the sensors are divided
        into 8 regions. See ``order`` kwarg of :func:`mne.viz.plot_raw`. If
        array, the channels are divided by picks given in the array.

        .. versionadded:: 0.13.0
    to_sphere : bool
        Whether to project the 3d locations to a sphere. When False, the
        sensor array appears similar as to looking downwards straight above the
        subject's head. Has no effect when kind='3d'. Defaults to True.

        .. versionadded:: 0.14.0
    axes : instance of Axes | instance of Axes3D | None
        Axes to draw the sensors to. If ``kind='3d'``, axes must be an instance
        of Axes3D. If None (default), a new axes will be created.

        .. versionadded:: 0.13.0
    block : bool
        Whether to halt program execution until the figure is closed. Defaults
        to False.

        .. versionadded:: 0.13.0
    show : bool
        Show figure if True. Defaults to True.
    %(topomap_sphere_auto)s
    %(verbose)s

    Returns
    -------
    fig : instance of Figure
        Figure containing the sensor topography.
    selection : list
        A list of selected channels. Only returned if ``kind=='select'``.

    See Also
    --------
    mne.viz.plot_layout

    Notes
    -----
    This function plots the sensor locations from the info structure using
    matplotlib. For drawing the sensors using mayavi see
    :func:`mne.viz.plot_alignment`.

    .. versionadded:: 0.12.0
    """
    from .evoked import _rgb
    _check_option('kind', kind, ['topomap', '3d', 'select'])
    if not isinstance(info, Info):
        raise TypeError('info must be an instance of Info not %s' % type(info))
    ch_indices = channel_indices_by_type(info)
    allowed_types = _DATA_CH_TYPES_SPLIT
    if ch_type is None:
        for this_type in allowed_types:
            if _contains_ch_type(info, this_type):
                ch_type = this_type
                break
        picks = ch_indices[ch_type]
    elif ch_type == 'all':
        picks = list()
        for this_type in allowed_types:
            picks += ch_indices[this_type]
    elif ch_type in allowed_types:
        picks = ch_indices[ch_type]
    else:
        raise ValueError("ch_type must be one of %s not %s!" % (allowed_types,
                                                                ch_type))

    if len(picks) == 0:
        raise ValueError('Could not find any channels of type %s.' % ch_type)

    chs = [info['chs'][pick] for pick in picks]
    if not _check_ch_locs(chs):
        raise RuntimeError('No valid channel positions found')
    dev_head_t = info['dev_head_t']
    pos = np.empty((len(chs), 3))
    for ci, ch in enumerate(chs):
        pos[ci] = ch['loc'][:3]
        if ch['coord_frame'] == FIFF.FIFFV_COORD_DEVICE:
            if dev_head_t is None:
                warn('dev_head_t is None, transforming MEG sensors to head '
                     'coordinate frame using identity transform')
                dev_head_t = np.eye(4)
            pos[ci] = apply_trans(dev_head_t, pos[ci])
    del dev_head_t

    ch_names = np.array([ch['ch_name'] for ch in chs])
    bads = [idx for idx, name in enumerate(ch_names) if name in info['bads']]
    if ch_groups is None:
        def_colors = _handle_default('color')
        colors = ['red' if i in bads else def_colors[channel_type(info, pick)]
                  for i, pick in enumerate(picks)]
    else:
        if ch_groups in ['position', 'selection']:
            if ch_groups == 'position':
                ch_groups = _divide_to_regions(info, add_stim=False)
                ch_groups = list(ch_groups.values())
            else:
                ch_groups, color_vals = list(), list()
                for selection in _SELECTIONS + _EEG_SELECTIONS:
                    channels = pick_channels(
                        info['ch_names'], read_selection(selection, info=info))
                    ch_groups.append(channels)
            color_vals = np.ones((len(ch_groups), 4))
            for idx, ch_group in enumerate(ch_groups):
                color_picks = [np.where(picks == ch)[0][0] for ch in ch_group
                               if ch in picks]
                if len(color_picks) == 0:
                    continue
                x, y, z = pos[color_picks].T
                color = np.mean(_rgb(x, y, z), axis=0)
                color_vals[idx, :3] = color  # mean of spatial color
        else:
            import matplotlib.pyplot as plt
            colors = np.linspace(0, 1, len(ch_groups))
            color_vals = [plt.cm.jet(colors[i]) for i in range(len(ch_groups))]
        if not isinstance(ch_groups, (np.ndarray, list)):
            raise ValueError("ch_groups must be None, 'position', "
                             "'selection', or an array. Got %s." % ch_groups)
        colors = np.zeros((len(picks), 4))
        for pick_idx, pick in enumerate(picks):
            for ind, value in enumerate(ch_groups):
                if pick in value:
                    colors[pick_idx] = color_vals[ind]
                    break
    title = 'Sensor positions (%s)' % ch_type if title is None else title
    fig = _plot_sensors(pos, info, picks, colors, bads, ch_names, title,
                        show_names, axes, show, kind, block,
                        to_sphere, sphere)
    if kind == 'select':
        return fig, fig.lasso.selection
    return fig


def _onpick_sensor(event, fig, ax, pos, ch_names, show_names):
    """Pick a channel in plot_sensors."""
    if event.mouseevent.inaxes != ax:
        return

    if event.mouseevent.key == 'control' and fig.lasso is not None:
        for ind in event.ind:
            fig.lasso.select_one(ind)

        return
    if show_names:
        return  # channel names already visible
    ind = event.ind[0]  # Just take the first sensor.
    ch_name = ch_names[ind]

    this_pos = pos[ind]

    # XXX: Bug in matplotlib won't allow setting the position of existing
    # text item, so we create a new one.
    ax.texts.pop(0)
    if len(this_pos) == 3:
        ax.text(this_pos[0], this_pos[1], this_pos[2], ch_name)
    else:
        ax.text(this_pos[0], this_pos[1], ch_name)
    fig.canvas.draw()


def _close_event(event, fig):
    """Listen for sensor plotter close event."""
    if getattr(fig, 'lasso', None) is not None:
        fig.lasso.disconnect()


def _plot_sensors(pos, info, picks, colors, bads, ch_names, title, show_names,
                  ax, show, kind, block, to_sphere, sphere):
    """Plot sensors."""
    from matplotlib import rcParams
    import matplotlib.pyplot as plt
    from mpl_toolkits.mplot3d import Axes3D
    from .topomap import _get_pos_outlines, _draw_outlines
    sphere = _check_sphere(sphere, info)

    edgecolors = np.repeat(rcParams['axes.edgecolor'], len(colors))
    edgecolors[bads] = 'red'
    axes_was_none = ax is None
    if axes_was_none:
        fig = plt.figure(figsize=(max(rcParams['figure.figsize']),) * 2)
        if kind == '3d':
            Axes3D(fig)
            ax = fig.gca(projection='3d')
        else:
            ax = fig.add_subplot(111)
    else:
        fig = ax.get_figure()

    if kind == '3d':
        ax.text(0, 0, 0, '', zorder=1)
        ax.scatter(pos[:, 0], pos[:, 1], pos[:, 2], picker=True, c=colors,
                   s=75, edgecolor=edgecolors, linewidth=2)

        ax.azim = 90
        ax.elev = 0
        ax.xaxis.set_label_text('x (m)')
        ax.yaxis.set_label_text('y (m)')
        ax.zaxis.set_label_text('z (m)')
    else:  # kind in 'select', 'topomap'
        ax.text(0, 0, '', zorder=1)

        pos, outlines = _get_pos_outlines(info, picks, sphere,
                                          to_sphere=to_sphere)
        _draw_outlines(ax, outlines)
        pts = ax.scatter(pos[:, 0], pos[:, 1], picker=True, clip_on=False,
                         c=colors, edgecolors=edgecolors, s=25, lw=2)
        if kind == 'select':
            fig.lasso = SelectFromCollection(ax, pts, ch_names)
        else:
            fig.lasso = None

        # Equal aspect for 3D looks bad, so only use for 2D
        ax.set(aspect='equal')
        if axes_was_none:
            fig.subplots_adjust(left=0, bottom=0, right=1, top=1, wspace=None,
                                hspace=None)
        ax.axis("off")  # remove border around figure
    del sphere

    connect_picker = True
    if show_names:
        if isinstance(show_names, (list, np.ndarray)):  # only given channels
            indices = [list(ch_names).index(name) for name in show_names]
        else:  # all channels
            indices = range(len(pos))
        for idx in indices:
            this_pos = pos[idx]
            if kind == '3d':
                ax.text(this_pos[0], this_pos[1], this_pos[2], ch_names[idx])
            else:
                ax.text(this_pos[0] + 0.0025, this_pos[1], ch_names[idx],
                        ha='left', va='center')
        connect_picker = (kind == 'select')
    if connect_picker:
        picker = partial(_onpick_sensor, fig=fig, ax=ax, pos=pos,
                         ch_names=ch_names, show_names=show_names)
        fig.canvas.mpl_connect('pick_event', picker)

    ax.set(title=title)
    closed = partial(_close_event, fig=fig)
    fig.canvas.mpl_connect('close_event', closed)
    plt_show(show, block=block)
    return fig


def _compute_scalings(scalings, inst, remove_dc=False, duration=10):
    """Compute scalings for each channel type automatically.

    Parameters
    ----------
    scalings : dict
        The scalings for each channel type. If any values are
        'auto', this will automatically compute a reasonable
        scaling for that channel type. Any values that aren't
        'auto' will not be changed.
    inst : instance of Raw or Epochs
        The data for which you want to compute scalings. If data
        is not preloaded, this will read a subset of times / epochs
        up to 100mb in size in order to compute scalings.
    remove_dc : bool
        Whether to remove the mean (DC) before calculating the scalings. If
        True, the mean will be computed and subtracted for short epochs in
        order to compensate not only for global mean offset, but also for slow
        drifts in the signals.
    duration : float
        If remove_dc is True, the mean will be computed and subtracted on
        segments of length ``duration`` seconds.

    Returns
    -------
    scalings : dict
        A scalings dictionary with updated values
    """
    from ..io.base import BaseRaw
    from ..epochs import BaseEpochs
    scalings = _handle_default('scalings_plot_raw', scalings)
    if not isinstance(inst, (BaseRaw, BaseEpochs)):
        raise ValueError('Must supply either Raw or Epochs')

    ch_types = channel_indices_by_type(inst.info)
    ch_types = {i_type: i_ixs
                for i_type, i_ixs in ch_types.items() if len(i_ixs) != 0}
    scalings = deepcopy(scalings)

    if inst.preload is False:
        if isinstance(inst, BaseRaw):
            # Load a window of data from the center up to 100mb in size
            n_times = 1e8 // (len(inst.ch_names) * 8)
            n_times = np.clip(n_times, 1, inst.n_times)
            n_secs = n_times / float(inst.info['sfreq'])
            time_middle = np.mean(inst.times)
            tmin = np.clip(time_middle - n_secs / 2., inst.times.min(), None)
            tmax = np.clip(time_middle + n_secs / 2., None, inst.times.max())
            data = inst._read_segment(tmin, tmax)
        elif isinstance(inst, BaseEpochs):
            # Load a random subset of epochs up to 100mb in size
            n_epochs = 1e8 // (len(inst.ch_names) * len(inst.times) * 8)
            n_epochs = int(np.clip(n_epochs, 1, len(inst)))
            ixs_epochs = np.random.choice(range(len(inst)), n_epochs, False)
            inst = inst.copy()[ixs_epochs].load_data()
    else:
        data = inst._data
    if isinstance(inst, BaseEpochs):
        data = inst._data.swapaxes(0, 1).reshape([len(inst.ch_names), -1])
    # Iterate through ch types and update scaling if ' auto'
    for key, value in scalings.items():
        if key not in ch_types:
            continue
        if not (isinstance(value, str) and value == 'auto'):
            try:
                scalings[key] = float(value)
            except Exception:
                raise ValueError(
                    f'scalings must be "auto" or float, got scalings[{key!r}]='
                    f'{value!r} which could not be converted to float')
            continue
        this_data = data[ch_types[key]]
        if remove_dc and (this_data.shape[1] / inst.info["sfreq"] >= duration):
            length = int(duration * inst.info["sfreq"])  # segment length
            # truncate data so that we can divide into segments of equal length
            this_data = this_data[:, :this_data.shape[1] // length * length]
            shape = this_data.shape  # original shape
            this_data = this_data.T.reshape(-1, length, shape[0])  # segment
            this_data -= np.nanmean(this_data, 0)  # subtract segment means
            this_data = this_data.T.reshape(shape)  # reshape into original
        this_data = this_data.ravel()
        this_data = this_data[np.isfinite(this_data)]
        if this_data.size:
            iqr = np.diff(np.percentile(this_data, [25, 75]))[0]
        else:
            iqr = 1.
        scalings[key] = iqr
    return scalings


def _setup_cmap(cmap, n_axes=1, norm=False):
    """Set color map interactivity."""
    if cmap == 'interactive':
        cmap = ('Reds' if norm else 'RdBu_r', True)
    elif not isinstance(cmap, tuple):
        if cmap is None:
            cmap = 'Reds' if norm else 'RdBu_r'
        cmap = (cmap, False if n_axes > 2 else True)
    return cmap


def _prepare_joint_axes(n_maps, figsize=None):
    """Prepare axes for topomaps and colorbar in joint plot figure.

    Parameters
    ----------
    n_maps: int
        Number of topomaps to include in the figure
    figsize: tuple
        Figure size, see plt.figsize

    Returns
    -------
    fig : matplotlib.figure.Figure
        Figure with initialized axes
    main_ax: matplotlib.axes._subplots.AxesSubplot
        Axes in which to put the main plot
    map_ax: list
        List of axes for each topomap
    cbar_ax: matplotlib.axes._subplots.AxesSubplot
        Axes for colorbar next to topomaps
    """
    import matplotlib.pyplot as plt
    fig = plt.figure(figsize=figsize)
    main_ax = fig.add_subplot(212)
    ts = n_maps + 2
    map_ax = [plt.subplot(4, ts, x + 2 + ts) for x in range(n_maps)]
    # Position topomap subplots on the second row, starting on the
    # second column
    cbar_ax = plt.subplot(4, 5 * (ts + 1), 10 * (ts + 1))
    # Position colorbar at the very end of a more finely divided
    # second row of subplots
    return fig, main_ax, map_ax, cbar_ax


class DraggableColorbar(object):
    """Enable interactive colorbar.

    See http://www.ster.kuleuven.be/~pieterd/python/html/plotting/interactive_colorbar.html
    """  # noqa: E501

    def __init__(self, cbar, mappable):
        import matplotlib.pyplot as plt
        self.cbar = cbar
        self.mappable = mappable
        self.press = None
        self.cycle = sorted([i for i in dir(plt.cm) if
                             hasattr(getattr(plt.cm, i), 'N')])
        self.cycle += [mappable.get_cmap().name]
        self.index = self.cycle.index(mappable.get_cmap().name)
        self.lims = (self.cbar.norm.vmin, self.cbar.norm.vmax)
        self.connect()

    def connect(self):
        """Connect to all the events we need."""
        self.cidpress = self.cbar.patch.figure.canvas.mpl_connect(
            'button_press_event', self.on_press)
        self.cidrelease = self.cbar.patch.figure.canvas.mpl_connect(
            'button_release_event', self.on_release)
        self.cidmotion = self.cbar.patch.figure.canvas.mpl_connect(
            'motion_notify_event', self.on_motion)
        self.keypress = self.cbar.patch.figure.canvas.mpl_connect(
            'key_press_event', self.key_press)
        self.scroll = self.cbar.patch.figure.canvas.mpl_connect(
            'scroll_event', self.on_scroll)

    def on_press(self, event):
        """Handle button press."""
        if event.inaxes != self.cbar.ax:
            return
        self.press = event.y

    def key_press(self, event):
        """Handle key press."""
        # print(event.key)
        scale = self.cbar.norm.vmax - self.cbar.norm.vmin
        perc = 0.03
        if event.key == 'down':
            self.index += 1
        elif event.key == 'up':
            self.index -= 1
        elif event.key == ' ':  # space key resets scale
            self.cbar.norm.vmin = self.lims[0]
            self.cbar.norm.vmax = self.lims[1]
        elif event.key == '+':
            self.cbar.norm.vmin -= (perc * scale) * -1
            self.cbar.norm.vmax += (perc * scale) * -1
        elif event.key == '-':
            self.cbar.norm.vmin -= (perc * scale) * 1
            self.cbar.norm.vmax += (perc * scale) * 1
        elif event.key == 'pageup':
            self.cbar.norm.vmin -= (perc * scale) * 1
            self.cbar.norm.vmax -= (perc * scale) * 1
        elif event.key == 'pagedown':
            self.cbar.norm.vmin -= (perc * scale) * -1
            self.cbar.norm.vmax -= (perc * scale) * -1
        else:
            return
        if self.index < 0:
            self.index = len(self.cycle) - 1
        elif self.index >= len(self.cycle):
            self.index = 0
        cmap = self.cycle[self.index]
        self.cbar.mappable.set_cmap(cmap)
        self.cbar.draw_all()
        self.mappable.set_cmap(cmap)
        self._update()

    def on_motion(self, event):
        """Handle mouse movements."""
        if self.press is None:
            return
        if event.inaxes != self.cbar.ax:
            return
        yprev = self.press
        dy = event.y - yprev
        self.press = event.y
        scale = self.cbar.norm.vmax - self.cbar.norm.vmin
        perc = 0.03
        if event.button == 1:
            self.cbar.norm.vmin -= (perc * scale) * np.sign(dy)
            self.cbar.norm.vmax -= (perc * scale) * np.sign(dy)
        elif event.button == 3:
            self.cbar.norm.vmin -= (perc * scale) * np.sign(dy)
            self.cbar.norm.vmax += (perc * scale) * np.sign(dy)
        self._update()

    def on_release(self, event):
        """Handle release."""
        self.press = None
        self._update()

    def on_scroll(self, event):
        """Handle scroll."""
        scale = 1.1 if event.step < 0 else 1. / 1.1
        self.cbar.norm.vmin *= scale
        self.cbar.norm.vmax *= scale
        self._update()

    def _update(self):
        self.cbar.set_ticks(None, update_ticks=True)  # use default
        self.cbar.draw_all()
        self.mappable.set_norm(self.cbar.norm)
        self.cbar.patch.figure.canvas.draw()


class SelectFromCollection(object):
    """Select channels from a matplotlib collection using ``LassoSelector``.

    Selected channels are saved in the ``selection`` attribute. This tool
    highlights selected points by fading other points out (i.e., reducing their
    alpha values).

    Parameters
    ----------
    ax : instance of Axes
        Axes to interact with.
    collection : instance of matplotlib collection
        Collection you want to select from.
    alpha_other : 0 <= float <= 1
        To highlight a selection, this tool sets all selected points to an
        alpha value of 1 and non-selected points to ``alpha_other``.
        Defaults to 0.3.
    linewidth_other : float
        Linewidth to use for non-selected sensors. Default is 1.

    Notes
    -----
    This tool selects collection objects based on their *origins*
    (i.e., ``offsets``). Emits mpl event 'lasso_event' when selection is ready.
    """

    def __init__(self, ax, collection, ch_names, alpha_other=0.5,
                 linewidth_other=0.5, alpha_selected=1, linewidth_selected=1):
        from matplotlib import __version__
        if LooseVersion(__version__) < LooseVersion('1.2.1'):
            raise ImportError('Interactive selection not possible for '
                              'matplotlib versions < 1.2.1. Upgrade '
                              'matplotlib.')
        from matplotlib.widgets import LassoSelector
        self.canvas = ax.figure.canvas
        self.collection = collection
        self.ch_names = ch_names
        self.alpha_other = alpha_other
        self.linewidth_other = linewidth_other
        self.alpha_selected = alpha_selected
        self.linewidth_selected = linewidth_selected

        self.xys = collection.get_offsets()
        self.Npts = len(self.xys)

        # Ensure that we have separate colors for each object
        self.fc = collection.get_facecolors()
        self.ec = collection.get_edgecolors()
        self.lw = collection.get_linewidths()
        if len(self.fc) == 0:
            raise ValueError('Collection must have a facecolor')
        elif len(self.fc) == 1:
            self.fc = np.tile(self.fc, self.Npts).reshape(self.Npts, -1)
            self.ec = np.tile(self.ec, self.Npts).reshape(self.Npts, -1)
        self.fc[:, -1] = self.alpha_other  # deselect in the beginning
        self.ec[:, -1] = self.alpha_other
        self.lw = np.full(self.Npts, self.linewidth_other)

        self.lasso = LassoSelector(ax, onselect=self.on_select,
                                   lineprops=dict(color='red', linewidth=0.5))
        self.selection = list()

    def on_select(self, verts):
        """Select a subset from the collection."""
        from matplotlib.path import Path
        if len(verts) <= 3:  # Seems to be a good way to exclude single clicks.
            return

        path = Path(verts)
        inds = np.nonzero([path.contains_point(xy) for xy in self.xys])[0]
        if self.canvas._key == 'control':  # Appending selection.
            sels = [np.where(self.ch_names == c)[0][0] for c in self.selection]
            inters = set(inds) - set(sels)
            inds = list(inters.union(set(sels) - set(inds)))

        self.selection[:] = np.array(self.ch_names)[inds].tolist()
        self.style_sensors(inds)
        self.canvas.callbacks.process('lasso_event')

    def select_one(self, ind):
        """Select or deselect one sensor."""
        ch_name = self.ch_names[ind]
        if ch_name in self.selection:
            sel_ind = self.selection.index(ch_name)
            self.selection.pop(sel_ind)
        else:
            self.selection.append(ch_name)
        inds = np.in1d(self.ch_names, self.selection).nonzero()[0]
        self.style_sensors(inds)
        self.canvas.callbacks.process('lasso_event')

    def select_many(self, inds):
        """Select many sensors using indices (for predefined selections)."""
        self.selection[:] = np.array(self.ch_names)[inds].tolist()
        self.style_sensors(inds)

    def style_sensors(self, inds):
        """Style selected sensors as "active"."""
        # reset
        self.fc[:, -1] = self.alpha_other
        self.ec[:, -1] = self.alpha_other / 2
        self.lw[:] = self.linewidth_other
        # style sensors at `inds`
        self.fc[inds, -1] = self.alpha_selected
        self.ec[inds, -1] = self.alpha_selected
        self.lw[inds] = self.linewidth_selected
        self.collection.set_facecolors(self.fc)
        self.collection.set_edgecolors(self.ec)
        self.collection.set_linewidths(self.lw)
        self.canvas.draw_idle()

    def disconnect(self):
        """Disconnect the lasso selector."""
        self.lasso.disconnect_events()
        self.fc[:, -1] = self.alpha_selected
        self.ec[:, -1] = self.alpha_selected
        self.collection.set_facecolors(self.fc)
        self.collection.set_edgecolors(self.ec)
        self.canvas.draw_idle()


def _get_color_list(annotations=False):
    """Get the current color list from matplotlib rcParams.

    Parameters
    ----------
    annotations : boolean
        Has no influence on the function if false. If true, check if color
        "red" (#ff0000) is in the cycle and remove it.

    Returns
    -------
    colors : list
    """
    from matplotlib import rcParams
    color_cycle = rcParams.get('axes.prop_cycle')

    if not color_cycle:
        # Use deprecated color_cycle to avoid KeyErrors in environments
        # with Python 2.7 and Matplotlib < 1.5
        # this will already be a list
        colors = rcParams.get('axes.color_cycle')
    else:
        # we were able to use the prop_cycle. Now just convert to list
        colors = color_cycle.by_key()['color']

    # If we want annotations, red is reserved ... remove if present. This
    # checks for the reddish color in MPL dark background style, normal style,
    # and MPL "red", and defaults to the last of those if none are present
    for red in ('#fa8174', '#d62728', '#ff0000'):
        if annotations and red in colors:
            colors.remove(red)
            break

    return (colors, red) if annotations else colors


def _merge_annotations(start, stop, description, annotations, current=()):
    """Handle drawn annotations."""
    ends = annotations.onset + annotations.duration
    idx = np.intersect1d(np.where(ends >= start)[0],
                         np.where(annotations.onset <= stop)[0])
    idx = np.intersect1d(idx,
                         np.where(annotations.description == description)[0])
    new_idx = np.setdiff1d(idx, current)  # don't include modified annotation
    end = max(np.append((annotations.onset[new_idx] +
                         annotations.duration[new_idx]), stop))
    onset = min(np.append(annotations.onset[new_idx], start))
    duration = end - onset
    annotations.delete(idx)
    annotations.append(onset, duration, description)


def _connection_line(x, fig, sourceax, targetax, y=1.,
                     y_source_transform="transAxes"):
    """Connect source and target plots with a line.

    Connect source and target plots with a line, such as time series
    (source) and topolots (target). Primarily used for plot_joint
    functions.
    """
    from matplotlib.lines import Line2D
    trans_fig = fig.transFigure
    trans_fig_inv = fig.transFigure.inverted()

    xt, yt = trans_fig_inv.transform(targetax.transAxes.transform([.5, 0.]))
    xs, _ = trans_fig_inv.transform(sourceax.transData.transform([x, 0.]))
    _, ys = trans_fig_inv.transform(getattr(sourceax, y_source_transform
                                            ).transform([0., y]))

    return Line2D((xt, xs), (yt, ys), transform=trans_fig, color='grey',
                  linestyle='-', linewidth=1.5, alpha=.66, zorder=1,
                  clip_on=False)


class DraggableLine(object):
    """Custom matplotlib line for moving around by drag and drop.

    Parameters
    ----------
    line : instance of matplotlib Line2D
        Line to add interactivity to.
    callback : function
        Callback to call when line is released.
    """

    def __init__(self, line, modify_callback, drag_callback):
        self.line = line
        self.press = None
        self.x0 = line.get_xdata()[0]
        self.modify_callback = modify_callback
        self.drag_callback = drag_callback
        self.cidpress = self.line.figure.canvas.mpl_connect(
            'button_press_event', self.on_press)
        self.cidrelease = self.line.figure.canvas.mpl_connect(
            'button_release_event', self.on_release)
        self.cidmotion = self.line.figure.canvas.mpl_connect(
            'motion_notify_event', self.on_motion)

    def set_x(self, x):
        """Repoisition the line."""
        self.line.set_xdata([x, x])
        self.x0 = x

    def on_press(self, event):
        """Store button press if on top of the line."""
        if event.inaxes != self.line.axes or not self.line.contains(event)[0]:
            return
        x0 = self.line.get_xdata()
        y0 = self.line.get_ydata()
        self.press = x0, y0, event.xdata, event.ydata

    def on_motion(self, event):
        """Move the line on drag."""
        if self.press is None:
            return
        if event.inaxes != self.line.axes:
            return
        x0, y0, xpress, ypress = self.press
        dx = event.xdata - xpress
        self.line.set_xdata(x0 + dx)
        self.drag_callback((x0 + dx)[0])
        self.line.figure.canvas.draw()

    def on_release(self, event):
        """Handle release."""
        if event.inaxes != self.line.axes or self.press is None:
            return
        self.press = None
        self.line.figure.canvas.draw()
        self.modify_callback(self.x0, event.xdata)
        self.x0 = event.xdata

    def remove(self):
        """Remove the line."""
        self.line.figure.canvas.mpl_disconnect(self.cidpress)
        self.line.figure.canvas.mpl_disconnect(self.cidrelease)
        self.line.figure.canvas.mpl_disconnect(self.cidmotion)
        self.line.figure.axes[0].lines.remove(self.line)


def _setup_ax_spines(axes, vlines, xmin, xmax, ymin, ymax, invert_y=False,
                     unit=None, truncate_xaxis=True, truncate_yaxis=True,
                     skip_axlabel=False, hline=True):
    # don't show zero line if it coincides with x-axis (even if hline=True)
    if hline and ymin != 0.:
        axes.spines['top'].set_position('zero')
    else:
        axes.spines['top'].set_visible(False)
    # the axes can become very small with topo plotting. This prevents the
    # x-axis from shrinking to length zero if truncate_xaxis=True, by adding
    # new ticks that are nice round numbers close to (but less extreme than)
    # xmin and xmax
    vlines = [] if vlines is None else vlines
    xticks = _trim_ticks(axes.get_xticks(), xmin, xmax)
    xticks = np.array(sorted(set([x for x in xticks] + vlines)))
    if len(xticks) < 2:
        def log_fix(tval):
            exp = np.log10(np.abs(tval))
            return np.sign(tval) * 10 ** (np.fix(exp) - (exp < 0))
        xlims = np.array([xmin, xmax])
        temp_ticks = log_fix(xlims)
        closer_idx = np.argmin(np.abs(xlims - temp_ticks))
        further_idx = np.argmax(np.abs(xlims - temp_ticks))
        start_stop = [temp_ticks[closer_idx], xlims[further_idx]]
        step = np.sign(np.diff(start_stop)) * np.max(np.abs(temp_ticks))
        tts = np.arange(*start_stop, step)
        xticks = np.array(sorted(xticks + [tts[0], tts[-1]]))
    axes.set_xticks(xticks)
    # y-axis is simpler
    yticks = _trim_ticks(axes.get_yticks(), ymin, ymax)
    axes.set_yticks(yticks)
    # truncation case 1: truncate both
    if truncate_xaxis and truncate_yaxis:
        axes.spines['bottom'].set_bounds(*xticks[[0, -1]])
        axes.spines['left'].set_bounds(*yticks[[0, -1]])
    # case 2: truncate only x (only right side; connect to y at left)
    elif truncate_xaxis:
        xbounds = np.array(axes.get_xlim())
        xbounds[1] = axes.get_xticks()[-1]
        axes.spines['bottom'].set_bounds(*xbounds)
    # case 3: truncate only y (only top; connect to x at bottom)
    elif truncate_yaxis:
        ybounds = np.array(axes.get_ylim())
        if invert_y:
            ybounds[0] = axes.get_yticks()[0]
        else:
            ybounds[1] = axes.get_yticks()[-1]
        axes.spines['left'].set_bounds(*ybounds)
    # handle axis labels
    if skip_axlabel:
        axes.set_yticklabels([''] * len(yticks))
        axes.set_xticklabels([''] * len(xticks))
    else:
        if unit is not None:
            axes.set_ylabel(unit, rotation=90)
        axes.set_xlabel('Time (s)')
    # plot vertical lines
    if vlines:
        _ymin, _ymax = axes.get_ylim()
        axes.vlines(vlines, _ymax, _ymin, linestyles='--', colors='k',
                    linewidth=1., zorder=1)
    # invert?
    if invert_y:
        axes.invert_yaxis()
    # changes we always make:
    axes.tick_params(direction='out')
    axes.tick_params(right=False)
    axes.spines['right'].set_visible(False)
    axes.spines['left'].set_zorder(0)


def _handle_decim(info, decim, lowpass):
    """Handle decim parameter for plotters."""
    from ..evoked import _check_decim
    from ..utils import _ensure_int
    if isinstance(decim, str) and decim == 'auto':
        lp = info['sfreq'] if info['lowpass'] is None else info['lowpass']
        lp = min(lp, info['sfreq'] if lowpass is None else lowpass)
        info['lowpass'] = lp
        decim = max(int(info['sfreq'] / (lp * 3) + 1e-6), 1)
    decim = _ensure_int(decim, 'decim', must_be='an int or "auto"')
    if decim <= 0:
        raise ValueError('decim must be "auto" or a positive integer, got %s'
                         % (decim,))
    decim = _check_decim(info, decim, 0)[0]
    data_picks = _pick_data_channels(info, exclude=())
    return decim, data_picks


def _setup_plot_projector(info, noise_cov, proj=True, use_noise_cov=True,
                          nave=1):
    from ..cov import compute_whitener
    projector = np.eye(len(info['ch_names']))
    whitened_ch_names = []
    if noise_cov is not None and use_noise_cov:
        # any channels in noise_cov['bads'] but not in info['bads'] get
        # set to nan, which means that they are not plotted.
        data_picks = _pick_data_channels(info, with_ref_meg=False, exclude=())
        data_names = {info['ch_names'][pick] for pick in data_picks}
        # these can be toggled by the user
        bad_names = set(info['bads'])
        # these can't in standard pipelines be enabled (we always take the
        # union), so pretend they're not in cov at all
        cov_names = ((set(noise_cov['names']) & set(info['ch_names'])) -
                     set(noise_cov['bads']))
        # Actually compute the whitener only using the difference
        whiten_names = cov_names - bad_names
        whiten_picks = pick_channels(info['ch_names'], whiten_names)
        whiten_info = pick_info(info, whiten_picks)
        rank = _triage_rank_sss(whiten_info, [noise_cov])[1][0]
        whitener, whitened_ch_names = compute_whitener(
            noise_cov, whiten_info, rank=rank, verbose=False)
        whitener *= np.sqrt(nave)  # proper scaling for Evoked data
        assert set(whitened_ch_names) == whiten_names
        projector[whiten_picks, whiten_picks[:, np.newaxis]] = whitener
        # Now we need to change the set of "whitened" channels to include
        # all data channel names so that they are properly italicized.
        whitened_ch_names = data_names
        # We would need to set "bad_picks" to identity to show the traces
        # (but in gray), but here we don't need to because "projector"
        # starts out as identity. So all that is left to do is take any
        # *good* data channels that are not in the noise cov to be NaN
        nan_names = data_names - (bad_names | cov_names)
        # XXX conditional necessary because of annoying behavior of
        # pick_channels where an empty list means "all"!
        if len(nan_names) > 0:
            nan_picks = pick_channels(info['ch_names'], nan_names)
            projector[nan_picks] = np.nan
    elif proj:
        projector, _ = setup_proj(info, add_eeg_ref=False, verbose=False)
    return projector, whitened_ch_names


def _check_sss(info):
    """Check SSS history in info."""
    ch_used = [ch for ch in _DATA_CH_TYPES_SPLIT
               if _contains_ch_type(info, ch)]
    has_meg = 'mag' in ch_used and 'grad' in ch_used
    has_sss = (has_meg and len(info['proc_history']) > 0 and
               info['proc_history'][0].get('max_info') is not None)
    return ch_used, has_meg, has_sss


def _triage_rank_sss(info, covs, rank=None, scalings=None):
    rank = dict() if rank is None else rank
    scalings = _handle_default('scalings_cov_rank', scalings)

    # Only look at good channels
    picks = _pick_data_channels(info, with_ref_meg=False, exclude='bads')
    info = pick_info(info, picks)
    ch_used, has_meg, has_sss = _check_sss(info)
    if has_sss:
        if 'mag' in rank or 'grad' in rank:
            raise ValueError('When using SSS, pass "meg" to set the rank '
                             '(separate rank values for "mag" or "grad" are '
                             'meaningless).')
    elif 'meg' in rank:
        raise ValueError('When not using SSS, pass separate rank values '
                         'for "mag" and "grad" (do not use "meg").')

    picks_list = _picks_by_type(info, meg_combined=has_sss)
    if has_sss:
        # reduce ch_used to combined mag grad
        ch_used = list(zip(*picks_list))[0]
    # order pick list by ch_used (required for compat with plot_evoked)
    picks_list = [x for x, y in sorted(zip(picks_list, ch_used))]
    n_ch_used = len(ch_used)

    # make sure we use the same rank estimates for GFP and whitening

    picks_list2 = [k for k in picks_list]
    # add meg picks if needed.
    if has_meg:
        # append ("meg", picks_meg)
        picks_list2 += _picks_by_type(info, meg_combined=True)

    rank_list = []  # rank dict for each cov
    for cov in covs:
        # We need to add the covariance projectors, compute the projector,
        # and apply it, just like we will do in prepare_noise_cov, otherwise
        # we risk the rank estimates being incorrect (i.e., if the projectors
        # do not match).
        info_proj = info.copy()
        info_proj['projs'] += cov['projs']
        this_rank = {}
        # assemble rank dict for this cov, such that we have meg
        for ch_type, this_picks in picks_list2:
            # if we have already estimates / values for mag/grad but not
            # a value for meg, combine grad and mag.
            if ('mag' in this_rank and 'grad' in this_rank and
                    'meg' not in rank):
                this_rank['meg'] = this_rank['mag'] + this_rank['grad']
                # and we're done here
                break
            if rank.get(ch_type) is None:
                ch_names = [info['ch_names'][pick] for pick in this_picks]
                this_C = pick_channels_cov(cov, ch_names)
                this_estimated_rank = compute_rank(
                    this_C, scalings=scalings, info=info_proj)[ch_type]
                this_rank[ch_type] = this_estimated_rank
            elif rank.get(ch_type) is not None:
                this_rank[ch_type] = rank[ch_type]

        rank_list.append(this_rank)
    return n_ch_used, rank_list, picks_list, has_sss


def _check_cov(noise_cov, info):
    """Check the noise_cov for whitening and issue an SSS warning."""
    from ..cov import read_cov, Covariance
    if noise_cov is None:
        return None
    if isinstance(noise_cov, str):
        noise_cov = read_cov(noise_cov)
    if not isinstance(noise_cov, Covariance):
        raise TypeError('noise_cov must be a str or Covariance, got %s'
                        % (type(noise_cov),))
    if _check_sss(info)[2]:  # has_sss
        warn('Data have been processed with SSS, which changes the relative '
             'scaling of magnetometers and gradiometers when viewing data '
             'whitened by a noise covariance')
    return noise_cov


def _set_title_multiple_electrodes(title, combine, ch_names, max_chans=6,
                                   all=False, ch_type=None):
    """Prepare a title string for multiple electrodes."""
    if title is None:
        title = ", ".join(ch_names[:max_chans])
        ch_type = _channel_type_prettyprint.get(ch_type, ch_type)
        if ch_type is None:
            ch_type = "sensor"
        if len(ch_names) > 1:
            ch_type += "s"
        if all is True and isinstance(combine, str):
            combine = combine.capitalize()
            title = "{} of {} {}".format(
                combine, len(ch_names), ch_type)
        elif len(ch_names) > max_chans and combine != "gfp":
            logger.info("More than {} channels, truncating title ...".format(
                max_chans))
            title += ", ...\n({} of {} {})".format(
                combine, len(ch_names), ch_type,)
    return title


def _check_time_unit(time_unit, times):
    if not isinstance(time_unit, str):
        raise TypeError('time_unit must be str, got %s' % (type(time_unit),))
    if time_unit == 's':
        pass
    elif time_unit == 'ms':
        times = 1e3 * times
    else:
        raise ValueError("time_unit must be 's' or 'ms', got %r" % time_unit)
    return time_unit, times


def _plot_masked_image(ax, data, times, mask=None, yvals=None,
                       cmap="RdBu_r", vmin=None, vmax=None, ylim=None,
                       mask_style="both", mask_alpha=.25, mask_cmap="Greys",
                       yscale="linear"):
    """Plot a potentially masked (evoked, TFR, ...) 2D image."""
    from matplotlib import ticker, __version__ as mpl_version

    if mask_style is None and mask is not None:
        mask_style = "both"  # default
    draw_mask = mask_style in {"both", "mask"}
    draw_contour = mask_style in {"both", "contour"}
    if cmap is None:
        mask_cmap = cmap

    # mask param check and preparation
    if draw_mask is None:
        if mask is not None:
            draw_mask = True
        else:
            draw_mask = False
    if draw_contour is None:
        if mask is not None:
            draw_contour = True
        else:
            draw_contour = False
    if mask is None:
        if draw_mask:
            warn("`mask` is None, not masking the plot ...")
            draw_mask = False
        if draw_contour:
            warn("`mask` is None, not adding contour to the plot ...")
            draw_contour = False

    if draw_mask:
        if mask.shape != data.shape:
            raise ValueError(
                "The mask must have the same shape as the data, "
                "i.e., %s, not %s" % (data.shape, mask.shape))
        if draw_contour and yscale == "log":
            warn("Cannot draw contours with linear yscale yet ...")

    if yvals is None:  # for e.g. Evoked images
        yvals = np.arange(data.shape[0])
    # else, if TFR plot, yvals will be freqs

    # test yscale
    if yscale == 'log' and not yvals[0] > 0:
        raise ValueError('Using log scale for frequency axis requires all your'
                         ' frequencies to be positive (you cannot include'
                         ' the DC component (0 Hz) in the TFR).')

    if len(yvals) < 2 or yvals[0] == 0:
        yscale = 'linear'
    elif yscale != 'linear':
        ratio = yvals[1:] / yvals[:-1]
    if yscale == 'auto':
        if yvals[0] > 0 and np.allclose(ratio, ratio[0]):
            yscale = 'log'
        else:
            yscale = 'linear'

    # https://github.com/matplotlib/matplotlib/pull/9477
    if yscale == "log" and mpl_version == "2.1.0":
        warn("With matplotlib version 2.1.0, lines may not show up in "
             "`AverageTFR.plot_joint`. Upgrade to a more recent version.")

    if yscale == "log":  # pcolormesh for log scale
        # compute bounds between time samples
        time_lims, = centers_to_edges(times)
        log_yvals = np.concatenate([[yvals[0] / ratio[0]], yvals,
                                    [yvals[-1] * ratio[0]]])
        yval_lims = np.sqrt(log_yvals[:-1] * log_yvals[1:])

        # construct a time-yvaluency bounds grid
        time_mesh, yval_mesh = np.meshgrid(time_lims, yval_lims)

        if mask is not None:
            ax.pcolormesh(time_mesh, yval_mesh, data, cmap=mask_cmap,
                          vmin=vmin, vmax=vmax, alpha=mask_alpha)
            im = ax.pcolormesh(time_mesh, yval_mesh,
                               np.ma.masked_where(~mask, data), cmap=cmap,
                               vmin=vmin, vmax=vmax, alpha=1)
        else:
            im = ax.pcolormesh(time_mesh, yval_mesh, data, cmap=cmap,
                               vmin=vmin, vmax=vmax)
        if ylim is None:
            ylim = yval_lims[[0, -1]]
        if yscale == 'log':
            ax.set_yscale('log')
            ax.get_yaxis().set_major_formatter(ticker.ScalarFormatter())

        ax.yaxis.set_minor_formatter(ticker.NullFormatter())
        # get rid of minor ticks
        ax.yaxis.set_minor_locator(ticker.NullLocator())
        tick_vals = yvals[np.unique(np.linspace(
            0, len(yvals) - 1, 12).round().astype('int'))]
        ax.set_yticks(tick_vals)

    else:
        # imshow for linear because the y ticks are nicer
        # and the masked areas look better
        dt = np.median(np.diff(times)) / 2. if len(times) > 1 else 0.1
        dy = np.median(np.diff(yvals)) / 2. if len(yvals) > 1 else 0.5
        extent = [times[0] - dt, times[-1] + dt,
                  yvals[0] - dy, yvals[-1] + dy]
        im_args = dict(interpolation='nearest', origin='lower',
                       extent=extent, aspect='auto', vmin=vmin, vmax=vmax)

        if draw_mask:
            ax.imshow(data, alpha=mask_alpha, cmap=mask_cmap, **im_args)
            im = ax.imshow(
                np.ma.masked_where(~mask, data), cmap=cmap, **im_args)
        else:
            ax.imshow(data, cmap=cmap, **im_args)  # see #6481
            im = ax.imshow(data, cmap=cmap, **im_args)

        if draw_contour and np.unique(mask).size == 2:
            big_mask = np.kron(mask, np.ones((10, 10)))
            ax.contour(big_mask, colors=["k"], extent=extent,
                       linewidths=[.75], corner_mask=False,
                       antialiased=False, levels=[.5])
        time_lims = [extent[0], extent[1]]
        if ylim is None:
            ylim = [extent[2], extent[3]]

    ax.set_xlim(time_lims[0], time_lims[-1])
    ax.set_ylim(ylim)

    if (draw_mask or draw_contour) and mask is not None:
        if mask.all():
            t_end = ", all points masked)"
        else:
            fraction = 1 - (np.float64(mask.sum()) / np.float64(mask.size))
            t_end = ", %0.3g%% of points masked)" % (fraction * 100,)
    else:
        t_end = ")"

    return im, t_end


@fill_doc
def _make_combine_callable(combine):
    """Convert None or string values of ``combine`` into callables.

    Params
    ------
    %(combine)s
        If callable, the callable must accept one positional input (data of
        shape ``(n_epochs, n_channels, n_times)`` or ``(n_evokeds, n_channels,
        n_times)``) and return an :class:`array <numpy.ndarray>` of shape
        ``(n_epochs, n_times)`` or ``(n_evokeds, n_times)``.
    """
    if combine is None:
        combine = partial(np.squeeze, axis=1)
    elif isinstance(combine, str):
        combine_dict = {key: partial(getattr(np, key), axis=1)
                        for key in ('mean', 'median', 'std')}
        combine_dict['gfp'] = lambda data: np.sqrt((data ** 2).mean(axis=1))
        try:
            combine = combine_dict[combine]
        except KeyError:
            raise ValueError('"combine" must be None, a callable, or one of '
                             '"mean", "median", "std", or "gfp"; got {}'
                             ''.format(combine))
    return combine


def center_cmap(cmap, vmin, vmax, name="cmap_centered"):
    """Center given colormap (ranging from vmin to vmax) at value 0.

    Parameters
    ----------
    cmap : matplotlib.colors.Colormap
        The colormap to center around 0.
    vmin : float
        Minimum value in the data to map to the lower end of the colormap.
    vmax : float
        Maximum value in the data to map to the upper end of the colormap.
    name : str
        Name of the new colormap. Defaults to 'cmap_centered'.

    Returns
    -------
    cmap_centered : matplotlib.colors.Colormap
        The new colormap centered around 0.

    Notes
    -----
    This function can be used in situations where vmin and vmax are not
    symmetric around zero. Normally, this results in the value zero not being
    mapped to white anymore in many colormaps. Using this function, the value
    zero will be mapped to white even for asymmetric positive and negative
    value ranges. Note that this could also be achieved by re-normalizing a
    given colormap by subclassing matplotlib.colors.Normalize as described
    here:
    https://matplotlib.org/users/colormapnorms.html#custom-normalization-two-linear-ranges
    """  # noqa: E501
    from matplotlib.colors import LinearSegmentedColormap

    vzero = abs(vmin) / float(vmax - vmin)
    index_old = np.linspace(0, 1, cmap.N)
    index_new = np.hstack([np.linspace(0, vzero, cmap.N // 2, endpoint=False),
                           np.linspace(vzero, 1, cmap.N // 2)])

    colors = "red", "green", "blue", "alpha"
    cdict = {name: [] for name in colors}
    for old, new in zip(index_old, index_new):
        for color, name in zip(cmap(old), colors):
            cdict[name].append((new, color, color))
    return LinearSegmentedColormap(name, cdict)


def _convert_psds(psds, dB, estimate, scaling, unit, ch_names=None,
                  first_dim='channel'):
    """Convert PSDs to dB (if necessary) and appropriate units.

    The following table summarizes the relationship between the value of
    parameters ``dB`` and ``estimate``, and the type of plot and corresponding
    units.

    | dB    | estimate    | plot | units             |
    |-------+-------------+------+-------------------|
    | True  | 'power'     | PSD  | amp**2/Hz (dB)    |
    | True  | 'amplitude' | ASD  | amp/sqrt(Hz) (dB) |
    | True  | 'auto'      | PSD  | amp**2/Hz (dB)    |
    | False | 'power'     | PSD  | amp**2/Hz         |
    | False | 'amplitude' | ASD  | amp/sqrt(Hz)      |
    | False | 'auto'      | ASD  | amp/sqrt(Hz)      |

    where amp are the units corresponding to the variable, as specified by
    ``unit``.
    """
    _check_option('first_dim', first_dim, ['channel', 'epoch'])
    where = np.where(psds.min(1) <= 0)[0]
    if len(where) > 0:
        # Construct a helpful error message, depending on whether the first
        # dimension of `psds` are channels or epochs.
        if dB:
            bad_value = 'Infinite'
        else:
            bad_value = 'Zero'

        if first_dim == 'channel':
            bads = ', '.join(ch_names[ii] for ii in where)
        else:
            bads = ', '.join(str(ii) for ii in where)

        msg = f'{bad_value} value in PSD for {first_dim}{_pl(where)} {bads}.'
        if first_dim == 'channel':
            msg += '\nThese channels might be dead.'
        warn(msg, UserWarning)

    if estimate == 'auto':
        estimate = 'power' if dB else 'amplitude'

    if estimate == 'amplitude':
        np.sqrt(psds, out=psds)
        psds *= scaling
        ylabel = r'$\mathrm{%s/\sqrt{Hz}}$' % unit
    else:
        psds *= scaling * scaling
        if '/' in unit:
            unit = '(%s)' % unit
        ylabel = r'$\mathrm{%s²/Hz}$' % unit
    if dB:
        np.log10(np.maximum(psds, np.finfo(float).tiny), out=psds)
        psds *= 10
        ylabel += r'$\ \mathrm{(dB)}$'

    return ylabel


def _plot_psd(inst, fig, freqs, psd_list, picks_list, titles_list,
              units_list, scalings_list, ax_list, make_label, color, area_mode,
              area_alpha, dB, estimate, average, spatial_colors, xscale,
              line_alpha, sphere, xlabels_list):
    # helper function for plot_raw_psd and plot_epochs_psd
    from matplotlib.ticker import ScalarFormatter
    from .evoked import _plot_lines

    for key, ls in zip(['lowpass', 'highpass', 'line_freq'],
                       ['--', '--', '-.']):
        if inst.info[key] is not None:
            for ax in ax_list:
                ax.axvline(inst.info[key], color='k', linestyle=ls,
                           alpha=0.25, linewidth=2, zorder=2)
    if line_alpha is None:
        line_alpha = 1.0 if average else 0.75
    line_alpha = float(line_alpha)
    ylabels = list()
    for ii, (psd, picks, title, ax, scalings, units) in enumerate(zip(
            psd_list, picks_list, titles_list, ax_list,
            scalings_list, units_list)):
        ylabel = _convert_psds(psd, dB, estimate, scalings, units,
                               [inst.ch_names[pi] for pi in picks])
        ylabels.append(ylabel)
        del ylabel

        if average:
            # mean across channels
            psd_mean = np.mean(psd, axis=0)
            if area_mode == 'std':
                # std across channels
                psd_std = np.std(psd, axis=0)
                hyp_limits = (psd_mean - psd_std, psd_mean + psd_std)
            elif area_mode == 'range':
                hyp_limits = (np.min(psd, axis=0),
                              np.max(psd, axis=0))
            else:  # area_mode is None
                hyp_limits = None

            ax.plot(freqs, psd_mean, color=color, alpha=line_alpha,
                    linewidth=0.5)
            if hyp_limits is not None:
                ax.fill_between(freqs, hyp_limits[0], y2=hyp_limits[1],
                                facecolor=color, alpha=area_alpha)

    if not average:
        picks = np.concatenate(picks_list)
        psd_list = np.concatenate(psd_list)
        types = np.array(inst.get_channel_types(picks=picks))
        # Needed because the data do not match the info anymore.
        info = create_info([inst.ch_names[p] for p in picks],
                           inst.info['sfreq'], types)
        info['chs'] = [inst.info['chs'][p] for p in picks]
        info['dev_head_t'] = inst.info['dev_head_t']
        ch_types_used = list()
        for this_type in _VALID_CHANNEL_TYPES:
            if this_type in types:
                ch_types_used.append(this_type)
        assert len(ch_types_used) == len(ax_list)
        unit = ''
        units = {t: yl for t, yl in zip(ch_types_used, ylabels)}
        titles = {c: t for c, t in zip(ch_types_used, titles_list)}
        picks = np.arange(len(psd_list))
        if not spatial_colors:
            spatial_colors = color
        _plot_lines(psd_list, info, picks, fig, ax_list, spatial_colors,
                    unit, units=units, scalings=None, hline=None, gfp=False,
                    types=types, zorder='std', xlim=(freqs[0], freqs[-1]),
                    ylim=None, times=freqs, bad_ch_idx=[], titles=titles,
                    ch_types_used=ch_types_used, selectable=True, psd=True,
                    line_alpha=line_alpha, nave=None, time_unit='ms',
                    sphere=sphere)

    for ii, (ax, xlabel) in enumerate(zip(ax_list, xlabels_list)):
        ax.grid(True, linestyle=':')
        if xscale == 'log':
            ax.set(xscale='log')
            ax.set(xlim=[freqs[1] if freqs[0] == 0 else freqs[0], freqs[-1]])
            ax.get_xaxis().set_major_formatter(ScalarFormatter())
        else:  # xscale == 'linear'
            ax.set(xlim=(freqs[0], freqs[-1]))
        if make_label:
            ax.set(ylabel=ylabels[ii], title=titles_list[ii])
            if xlabel:
                ax.set_xlabel('Frequency (Hz)')

    if make_label:
        fig.align_ylabels(axs=ax_list)
    return fig


def _trim_ticks(ticks, _min, _max):
    """Remove ticks that are more extreme than the given limits."""
    keep = np.where(np.logical_and(ticks >= _min, ticks <= _max))
    return ticks[keep]


def _set_window_title(fig, title):
    if fig.canvas.manager is not None:
        fig.canvas.manager.set_window_title(title)


def _shorten_path_from_middle(fpath, max_len=60, replacement='...'):
    """Truncate a path from the middle by omitting complete path elements."""
    from os.path import sep
    if len(fpath) > max_len:
        pathlist = fpath.split(sep)
        # indices starting from middle, alternating sides, omitting final elem:
        # range(8) → 3, 4, 2, 5, 1, 6; range(7) → 2, 3, 1, 4, 0, 5
        ixs_to_trunc = list(zip(range(len(pathlist) // 2 - 1, -1, -1),
                                range(len(pathlist) // 2, len(pathlist) - 1)))
        ixs_to_trunc = np.array(ixs_to_trunc).flatten()
        for ix in ixs_to_trunc:
            pathlist[ix] = replacement
            truncs = (np.array(pathlist) == replacement).nonzero()[0]
            newpath = sep.join(pathlist[:truncs[0]] + pathlist[truncs[-1]:])
            if len(newpath) < max_len:
                break
        return newpath
    return fpath


def centers_to_edges(*arrays):
    """Convert center points to edges.

    Parameters
    ----------
    *arrays : list of ndarray
        Each input array should be 1D monotonically increasing,
        and will be cast to float.

    Returns
    -------
    arrays : list of ndarray
        Given each input of shape (N,), the output will have shape (N+1,).

    Examples
    --------
    >>> x = [0., 0.1, 0.2, 0.3]
    >>> y = [20, 30, 40]
    >>> centers_to_edges(x, y)  # doctest: +SKIP
    [array([-0.05, 0.05, 0.15, 0.25, 0.35]), array([15., 25., 35., 45.])]
    """
    out = list()
    for ai, arr in enumerate(arrays):
        arr = np.asarray(arr, dtype=float)
        _check_option(f'arrays[{ai}].ndim', arr.ndim, (1,))
        if len(arr) > 1:
            arr_diff = np.diff(arr) / 2.
        else:
            arr_diff = [abs(arr[0]) * 0.001] if arr[0] != 0 else [0.001]
        out.append(np.concatenate([
            [arr[0] - arr_diff[0]],
            arr[:-1] + arr_diff,
            [arr[-1] + arr_diff[-1]]]))
    return out